Painlevé analysis and new analytic solutions for (1+1)-dimensional higher-order Broer-Kaup system with symbolic computation

The (1+1)-dimensional higher-order Broer-Kaup (HBK) system is investigated in this paper. Painlevé test shows that there are two solution branches, one of which has the resonance -2. And an auto-Bäcklund transformation is obtained by the truncated Painlevé expansion. The new analytic solutions are presented by means of the auto-Bäcklund transformation, including the periodic and soliton-like solutions. Similarity reductions for the HBK system are given out to two ordinary differential equations (ODEs) through CK direct method.